Optimization problem

HIii, i have a math problem

A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, wheras the semicircle is of tinted glass and only transmits half the amount of light as the clear glass. The total perimeter is fixed. Find the proportions of the window that will admit the most light.

This is what i know so far

The overall perimeter will be perimeter of rectangle plus circumference of the semi-circle. P = (Pi)(R) + 4(Pi)+ 2H

Now we need to find area which will be area of half circle plus area of rectangle.

A = {(Pi)(r)^2}/4 + 2(Pi)(H)

now i know that we have to isolate for H in the perimeter formula and sub it into the area formula....but no numbers are given..how do i find proportions?? do i just sub in any number for P??

A window is in the form of a rectangle surmounted by a semicircle. The rectangle is of clear glass, wheras the semicircle is of tinted glass and only transmits half the amount of light as the clear glass. The total perimeter is fixed. Find the proportions of the window that will admit the most light.

This is what i know so far

The overall perimeter will be perimeter of rectangle plus circumference of the semi-circle. P = (Pi)(R) + 4(Pi)+ 2H

The perimeter is that of a semi circle , the two sides and the base for a total of: